Question

The parent secant function is shifted 2 units down, and its period is changed to pi. Which of the following is the graph of the transformed function?

Thank you!

Answer 1

The answer is graph D

Explanation:

Answer 2

The parent secant function is sec(x). The period of parent secant function in 2π.

Two transformations are applied to this function.

1st Transformation:
Function is shifted down by 2 units. The resultant function will be:

sec(x) - 2

2nd Transformation:
The period of function is changed to π. The resultant function after both transformations will be:

sec(2x) - 2

The graph of transformed function over 1 period is attached below.